Constraint Manifold Exploration for Efficient Continuous Coverage Estimation

TL;DR

This work addresses the challenge of determining whether a robot arm can continuously cover a surface while maintaining the tool orthogonal to the surface. It introduces an extended ambient configuration space that encodes position and orientation constraints and develops two sampling-based exploration strategies on an implicit constraint manifold to map reachable surface coordinates. By discretizing the surface domain and tracking sampled configurations, it yields an estimate of the continuously coverable region and demonstrates favorable runtime and coverage characteristics across diverse robots and CAD-surfaces. The approach enables accurate feasibility analysis and can seed region-based tool-path planning for complex industrial surfaces, with potential extensions to direct coverage CPP and enhanced performance metrics.

Abstract

Many automated manufacturing processes rely on industrial robot arms to move process-specific tools along workpiece surfaces. In applications like grinding, sanding, spray painting, or inspection, they need to cover a workpiece fully while keeping their tools perpendicular to its surface. While there are approaches to generate trajectories for these applications, there are no sufficient methods for analyzing the feasibility of full surface coverage. This work proposes a sampling-based approach for continuous coverage estimation that explores reachable surface regions in the configuration space. We define an extended ambient configuration space that allows for the representation of tool position and orientation constraints. A continuation-based approach is used to explore it using two different sampling strategies. A thorough evaluation across different kinematics and environments analyzes their runtime and efficiency. This validates our ability to accurately and efficiently calculate surface coverage for complex surfaces in complicated environments.

Figures (7)

• Figure 1: Continuous coverage of a surface by a robot using the proposed approach. Starting from an initial configuration, continuous paths across the surface are explored. Reachable surface cells are colored based on their exploration order and some configurations near the border are overlaid.
• Figure 2: Continuous coverage estimation by configuration space manifold exploration. Continuous motions of the robot on the left along the surface $S$ form a smooth manifold $\mathcal{M}_S$ on the right. Starting from an initial configuration $q_0$, we explore the manifold using the configuration-space motions shown in green and project them to surface coordinates. Continually doing so increases the estimated coverable region $\hat{\mathcal{U}}_S$ until the blue region on the left is covered by samples.
• Figure 3: The matrix of robots and environments used throughout the evaluation. We use two six-axis and one seven-axis robots to cover different relevant kinematics, and three surfaces with different curvatures and obstacles to achieve representative results. The icons next to each robot are used throughout the evaluation to reference specific setups.
• Figure 4: The results of the parameter evaluation. For both exploration approaches, the mean runtime and the mean coverage in percent of reachable cells across 25 experiments of 25000.0 samples are shown. The rows are organized in groups by scenario.
• Figure 5: Sampling behavior of the Kuka robot in the curved and maze environments after 100000.0 samples. The four images on the left visualize the number of samples per cell, while the right images show the exploration order. Spots of high sampling density were manually annotated.

Theorems & Definitions (2)

• Definition II.1: Surface-Constrained Configuration
• Definition II.2: Continuous Coverage Estimation